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The Liberal-Nationals MP called for proactive mental health services to try and identify and prevent serious sex offenders.

"We have a gendered violence crisis in this country," Ms Hutchins added.

Jaymes Todd, 19 of Broadmeadows, is charged with Ms Dixon's rape and murder.

The aspiring comedian was killed on her way home from performing a gig at Melbourne's Highlander Bar on June 12.

Thousands of people on Monday evening gathered for a solemn vigil at the Carlton park where her body was found.

Premier Daniel Andrews said the vigil was a tribute to not only Ms Dixon, but the spirit of Victorians sticking together in the worst of times.

"The death of Eurydice Dixon is not only a matter of great sadness, it is also a poignant reminder that when it comes to the safety of women, we have to do so much more," Mr Andrews told parliament on Tuesday.

"Bad outcomes, sometimes tragic outcomes, for women start with bad attitudes towards women and we have called that out. We have to continue to call that out, we have to continue to speak up."

Opposition leader Matthew Guy said women shouldn't have to spend time contemplating their safety.

"Enough is enough, we want our safe Melbourne back, we want these heinous crimes to stop," he said.

Melbourne's comedy community has released a song in Ms Dixon's memory, called Remembering Eurydice.

"We remember your life was sacred, remember that we love you," the lyrics say.

"If we're going to make sure crimes like that which occurred so heinously in Carlton don't occur, we're going to just have to get better, and much better, at respect in the community," he told ABC Melbourne radio.